//============================================================================================= // MadgwickAHRS.h //============================================================================================= // // Implementation of Madgwick's IMU and AHRS algorithms. // See: http://www.x-io.co.uk/open-source-imu-and-ahrs-algorithms/ // // From the x-io website "Open-source resources available on this website are // provided under the GNU General Public Licence unless an alternative licence // is provided in source." // // Date Author Notes // 29/09/2011 SOH Madgwick Initial release // 02/10/2011 SOH Madgwick Optimised for reduced CPU load // //============================================================================================= // 'ported' to processing class Madgwick{ float beta; // algorithm gain float q0; float q1; float q2; float q3; // quaternion of sensor frame relative to auxiliary frame float invSampleFreq; Madgwick(){ beta = 0.5f; //0.1f q0 = 1.0f; q1 = 0.0f; q2 = 0.0f; q3 = 0.0f; invSampleFreq = 1.0f / 512.0f; } void begin(float sampleFrequency) { invSampleFreq = 1.0f / sampleFrequency; } void update(float gx, float gy, float gz, float ax, float ay, float az, float mx, float my, float mz) { float recipNorm; float s0, s1, s2, s3; float qDot1, qDot2, qDot3, qDot4; float hx, hy; float _2q0mx, _2q0my, _2q0mz, _2q1mx, _2bx, _2bz, _4bx, _4bz, _2q0, _2q1, _2q2, _2q3, _2q0q2, _2q2q3, q0q0, q0q1, q0q2, q0q3, q1q1, q1q2, q1q3, q2q2, q2q3, q3q3; // Use IMU algorithm if magnetometer measurement invalid (avoids NaN in magnetometer normalisation) if((mx == 0.0f) && (my == 0.0f) && (mz == 0.0f)) { updateIMU(gx, gy, gz, ax, ay, az); return; } // Convert gyroscope degrees/sec to radians/sec gx *= 0.0174533f; gy *= 0.0174533f; gz *= 0.0174533f; // Rate of change of quaternion from gyroscope qDot1 = 0.5f * (-q1 * gx - q2 * gy - q3 * gz); qDot2 = 0.5f * (q0 * gx + q2 * gz - q3 * gy); qDot3 = 0.5f * (q0 * gy - q1 * gz + q3 * gx); qDot4 = 0.5f * (q0 * gz + q1 * gy - q2 * gx); // Compute feedback only if accelerometer measurement valid (avoids NaN in accelerometer normalisation) if(!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) { // Normalise accelerometer measurement recipNorm = 1.0f/sqrt(ax * ax + ay * ay + az * az); ax *= recipNorm; ay *= recipNorm; az *= recipNorm; // Normalise magnetometer measurement recipNorm = 1.0f/sqrt(mx * mx + my * my + mz * mz); mx *= recipNorm; my *= recipNorm; mz *= recipNorm; // Auxiliary variables to avoid repeated arithmetic _2q0mx = 2.0f * q0 * mx; _2q0my = 2.0f * q0 * my; _2q0mz = 2.0f * q0 * mz; _2q1mx = 2.0f * q1 * mx; _2q0 = 2.0f * q0; _2q1 = 2.0f * q1; _2q2 = 2.0f * q2; _2q3 = 2.0f * q3; _2q0q2 = 2.0f * q0 * q2; _2q2q3 = 2.0f * q2 * q3; q0q0 = q0 * q0; q0q1 = q0 * q1; q0q2 = q0 * q2; q0q3 = q0 * q3; q1q1 = q1 * q1; q1q2 = q1 * q2; q1q3 = q1 * q3; q2q2 = q2 * q2; q2q3 = q2 * q3; q3q3 = q3 * q3; // Reference direction of Earth's magnetic field hx = mx * q0q0 - _2q0my * q3 + _2q0mz * q2 + mx * q1q1 + _2q1 * my * q2 + _2q1 * mz * q3 - mx * q2q2 - mx * q3q3; hy = _2q0mx * q3 + my * q0q0 - _2q0mz * q1 + _2q1mx * q2 - my * q1q1 + my * q2q2 + _2q2 * mz * q3 - my * q3q3; _2bx = sqrt(hx * hx + hy * hy); _2bz = -_2q0mx * q2 + _2q0my * q1 + mz * q0q0 + _2q1mx * q3 - mz * q1q1 + _2q2 * my * q3 - mz * q2q2 + mz * q3q3; _4bx = 2.0f * _2bx; _4bz = 2.0f * _2bz; // Gradient decent algorithm corrective step s0 = -_2q2 * (2.0f * q1q3 - _2q0q2 - ax) + _2q1 * (2.0f * q0q1 + _2q2q3 - ay) - _2bz * q2 * (_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) + (-_2bx * q3 + _2bz * q1) * (_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) + _2bx * q2 * (_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz); s1 = _2q3 * (2.0f * q1q3 - _2q0q2 - ax) + _2q0 * (2.0f * q0q1 + _2q2q3 - ay) - 4.0f * q1 * (1 - 2.0f * q1q1 - 2.0f * q2q2 - az) + _2bz * q3 * (_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) + (_2bx * q2 + _2bz * q0) * (_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) + (_2bx * q3 - _4bz * q1) * (_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz); s2 = -_2q0 * (2.0f * q1q3 - _2q0q2 - ax) + _2q3 * (2.0f * q0q1 + _2q2q3 - ay) - 4.0f * q2 * (1 - 2.0f * q1q1 - 2.0f * q2q2 - az) + (-_4bx * q2 - _2bz * q0) * (_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) + (_2bx * q1 + _2bz * q3) * (_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) + (_2bx * q0 - _4bz * q2) * (_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz); s3 = _2q1 * (2.0f * q1q3 - _2q0q2 - ax) + _2q2 * (2.0f * q0q1 + _2q2q3 - ay) + (-_4bx * q3 + _2bz * q1) * (_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) + (-_2bx * q0 + _2bz * q2) * (_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) + _2bx * q1 * (_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz); recipNorm = 1.0f/sqrt(s0 * s0 + s1 * s1 + s2 * s2 + s3 * s3); // normalise step magnitude s0 *= recipNorm; s1 *= recipNorm; s2 *= recipNorm; s3 *= recipNorm; // Apply feedback step qDot1 -= beta * s0; qDot2 -= beta * s1; qDot3 -= beta * s2; qDot4 -= beta * s3; } // Integrate rate of change of quaternion to yield quaternion q0 += qDot1 * invSampleFreq; q1 += qDot2 * invSampleFreq; q2 += qDot3 * invSampleFreq; q3 += qDot4 * invSampleFreq; // Normalise quaternion recipNorm = 1.0f/sqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3); q0 *= recipNorm; q1 *= recipNorm; q2 *= recipNorm; q3 *= recipNorm; } void updateIMU(float gx, float gy, float gz, float ax, float ay, float az) { float recipNorm; float s0, s1, s2, s3; float qDot1, qDot2, qDot3, qDot4; float _2q0, _2q1, _2q2, _2q3, _4q0, _4q1, _4q2 ,_8q1, _8q2, q0q0, q1q1, q2q2, q3q3; // Convert gyroscope degrees/sec to radians/sec gx *= 0.0174533f; gy *= 0.0174533f; gz *= 0.0174533f; // Rate of change of quaternion from gyroscope qDot1 = 0.5f * (-q1 * gx - q2 * gy - q3 * gz); qDot2 = 0.5f * (q0 * gx + q2 * gz - q3 * gy); qDot3 = 0.5f * (q0 * gy - q1 * gz + q3 * gx); qDot4 = 0.5f * (q0 * gz + q1 * gy - q2 * gx); // Compute feedback only if accelerometer measurement valid (avoids NaN in accelerometer normalisation) if(!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) { // Normalise accelerometer measurement recipNorm = 1.0f/sqrt(ax * ax + ay * ay + az * az); ax *= recipNorm; ay *= recipNorm; az *= recipNorm; // Auxiliary variables to avoid repeated arithmetic _2q0 = 2.0f * q0; _2q1 = 2.0f * q1; _2q2 = 2.0f * q2; _2q3 = 2.0f * q3; _4q0 = 4.0f * q0; _4q1 = 4.0f * q1; _4q2 = 4.0f * q2; _8q1 = 8.0f * q1; _8q2 = 8.0f * q2; q0q0 = q0 * q0; q1q1 = q1 * q1; q2q2 = q2 * q2; q3q3 = q3 * q3; // Gradient decent algorithm corrective step s0 = _4q0 * q2q2 + _2q2 * ax + _4q0 * q1q1 - _2q1 * ay; s1 = _4q1 * q3q3 - _2q3 * ax + 4.0f * q0q0 * q1 - _2q0 * ay - _4q1 + _8q1 * q1q1 + _8q1 * q2q2 + _4q1 * az; s2 = 4.0f * q0q0 * q2 + _2q0 * ax + _4q2 * q3q3 - _2q3 * ay - _4q2 + _8q2 * q1q1 + _8q2 * q2q2 + _4q2 * az; s3 = 4.0f * q1q1 * q3 - _2q1 * ax + 4.0f * q2q2 * q3 - _2q2 * ay; recipNorm = 1.0f/sqrt(s0 * s0 + s1 * s1 + s2 * s2 + s3 * s3); // normalise step magnitude s0 *= recipNorm; s1 *= recipNorm; s2 *= recipNorm; s3 *= recipNorm; // Apply feedback step qDot1 -= beta * s0; qDot2 -= beta * s1; qDot3 -= beta * s2; qDot4 -= beta * s3; } // Integrate rate of change of quaternion to yield quaternion q0 += qDot1 * invSampleFreq; q1 += qDot2 * invSampleFreq; q2 += qDot3 * invSampleFreq; q3 += qDot4 * invSampleFreq; // Normalise quaternion recipNorm = 1.0f/sqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3); q0 *= recipNorm; q1 *= recipNorm; q2 *= recipNorm; q3 *= recipNorm; } }